International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 369078, 15 pages
doi:10.1155/2010/369078
Research Article

Differential Subordination Defined by New Generalised Derivative Operator for Analytic Functions

Ma'moun Harayzeh Al-Abbadi and Maslina Darus

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi Selangor (Darul Ehsan), Malaysia

Received 9 June 2009; Revised 20 December 2009; Accepted 9 March 2010

Academic Editor: Dorothy Wallace

Copyright © 2010 Ma'moun Harayzeh Al-Abbadi and Maslina Darus. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new generalised derivative operator μλ1,λ2n,m is introduced. This operator generalised many well-known operators studied earlier by many authors. Using the technique of differential subordination, we will study some of the properties of differential subordination. In addition we investigate several interesting properties of the new generalised derivative operator.